# On the performance degradation of dominance-based evolutionary algorithms in many-objective optimization.

## Data

2018

## Título da Revista

## ISSN da Revista

## Título de Volume

## Editor

## Resumo

In the last decade, it has become apparent that the
performance of Pareto-dominance based evolutionary multiobjective optimization algorithms degrades as the number of objective
functions of the problem, given by n, grows. This performance
degradation has been the subject of several studies in the last
years, but the exact mechanism behind this phenomenon has
not been fully understood yet. This paper presents an analytical
study of this phenomenon under problems with continuous
variables, by a simple setup of quadratic objective functions
with spherical contour curves and a symmetrical arrangement
of the function minima location. Within such a setup, some
analytical formulae are derived to describe the probability of
the optimization progress as a function of the distance λ to the
exact Pareto-set. A main conclusion is stated about the nature and
structure of the performance degradation phenomenon in manyobjective problems: when a current solution reaches a λ that is
an order of magnitude smaller than the length of the Pareto-set,
the probability of finding a new point that dominates the current
one is given by a power law function of λ with exponent (n−1).
The dimension of the space of decision variables has no influence
on that exponent. Those results give support to a discussion about
some general directions that are currently under consideration
within the research community.

## Descrição

## Palavras-chave

Evolutionary computation, Many-objective problems

## Citação

SANTOS, T. F.; TAKAHASHI, R. H. C. On the performance degradation of dominance-based evolutionary algorithms in many-objective optimization. IEEE Transactions On Evolutionary Computation, v. 22, p. 1-13, 2018. Disponível em: <https://ieeexplore.ieee.org/document/7727968>. Acesso em: 19 mar. 2019.